THE HAnDbook of TECHnICAl AnAlysIsGeometric Expectancy = Return Ratio (1/T) = 0.9653(1/75)
= 0.99952 (i.e., <1)Therefore, we see that increasing the tradesize actually decreases the geometric
expectancy in this case and hence results in a loss. This is a very significant point.
It tells us that we can turn a winning system into a losing system by just increasing
the tradesize. It also tells us that there is a possibility that we may also be able to
turn a losing system into a winning system by just decreasing the tradesize.
For dynamic sizing, there exists an optimal %risk for every R/r ratio setup.
Crossing that threshold will cause a winning system to start losing money. The
trader must therefore know what that tradesize is before embarking on a cam-
paign of augmenting %risk and tradesizes in the hope of boosting profitability.
Minimum %Win for Dynamic sizing systems
Let wins equal W and losses equal L. To find the minimum wins required to return
to breakeven, set the return ratio to equal 1. (R = Reward ratio, r = Risk ratio, W
= number of wins, and L = number of losses)
Return Ratio R r
R r
W lnR L lnr
W L lnr lnRW L
W L=×=
=
=−
=−
−1
( / )
This represents the number of wins required to return to breakeven.effect of risksizing on Dynamic sizing systems
Let us now calculate the minimum %win for dynamic sizing system.
a. Let R/r → 2:1, %r = 10 percent and L = 49 losing trades:
W = −L (lnr/lnR)
W = −49 (ln0.9/ln1.2) = 28.31 wins required to break even
Minimum %win = (28.31/(28.31 + 49)) × 100% = 36.6%
b. Let R/r → 2:1, %r = 20 percent and L = 49 losing trades:
W = −49 (ln0.8/ln1.4) = 32.49 wins required to break even
Min %win = (32.49/(32.49 +49)) × 100% = 39.9%
We see that increasing the %risk actually increases the minimum %win, mak-
ing it harder to maintain a positive expectancy over the longer term.
We learned from studying the relationships between risk, tradesize, number of
trades, and R/r ratio sizing that:
■ (^) Increasing the number of trades when the geometric expectancy is less than
one is detrimental to the trading account
■ (^) Increasing the number of trades when the geometric expectancy is greater
than one is highly favorable to the trading account